Q 2. I don't know what you mean by a .mov file as it could be numerous things.
As for the mp4, as long as it is H.264 with AAC audio you should be able to put it on a flash thumbstick or USB 2.0 hard drive and have it play in a media player similar to the WD TV HD.
That's an HDV PAL Sequence.
Sounds like FCE is OK.
There are in/out settings on the Sony 700 that also need to be checked for incoming HDV.
HDV/DV set to HDV and iLink Conversion switched to OFF.
There is a delay while FCE prepares the export to tape but it sounds exessive in your case.
BTW: You don't need in/out points if the whole Timeline is being sent.